Carefully put the wrong side out sock on your fingers again (be gentle as runs may occur) and fold back the raw edge so that it lay on the wrong side (you will have to fold it back as you sew) and start a whip stitch around the edge in the same way as you did for the cuff. You can run a running stitch around the hole first to hold the edge where you want it, but in my experience the running stitch will have to be removed to allow the sock to stretch around your thumb.

Wrong side

Right side

Tie the ends off and you're good to go! This would be a good time to point out how much of my thumb sticks out of that TINY HOLE I cut earlier. Like I said, socks is stretchy.

Oh, and why to do with the rest of the sock? Make a big hair tie! I removed the toe and heel seam, folded the resulting tube in half with right side out, tri-folded it with the raw edges in the middle and added a couple knotted whip stitches about every inch to hold the ends together. Or you could just roll the tube from one end to the other (like how pantyhose roll up when you're taking them off) and leave the raw edge to fray naturally. I was kinda suprised at how good of a hair tie it is.

I admit I search the little kids section at the local thrifts looking for long sleeved shirts. They have much better colors and patterns than normal socks but are in the right 'tube' shape, plus I can hem the arms on the shirt and donate it back (in point of fact, a couple of the shirts I've done this to look MUCH better short-sleeved than they did long-sleeved).

And yes, fuzzy arm socks rock, but if it's really fuzzy, it's a pain to hem.